For any two statement p and q , the negative of the expression p ∨ ~ p ∧ q is

Step-by-step solution

~ p ∨ ~ p ∧ q Using ~ a ∨ b = ~ a ∧ ~ b ,   ~ a ∧ b = ~ a ∨ ~ b   &   ~ ~ a = a , we get = ~ p ∧ ~ ~ p ∧ q = ~ p ∧ ~ ~ p ∨ q = ∼ p ∧ p ∨ ∼ q Using distributive law, i.e. a ∧ b ∨ c = a ∧ b ∨ a ∧ c , we get = ~ p ∧ p ∨ ~ p ∧ ~ q Using ~ a ∧ a = C , where C represents contradiction, we get = C ∨ ~ p ∧ ~ q Using C ∨ a = a , we get = ~ p ∧ ~